Separable Lyapunov functions for monotone systems
Rantzer, Anders LU
; Rüffer, Björn
and Dirr, Gunther
(2013)
52nd IEEE Conference on Decision and Control, 2013
- Abstract
- Separable Lyapunov functions play vital roles, for example, in stability analysis of large-scale systems. A Lyapunov function is called max-separable if it can be decomposed into a maximum of functions with one-dimensional arguments. Similarly, it is called sum-separable if it is a sum of such functions. In this paper it is shown that for a monotone system on a compact state space, asymptotic stability implies existence of a max-separable Lyapunov function. We also construct two systems on a non-compact state space, for which a max- separable Lyapunov function does not exist. One of them has a sum-separable Lyapunov function. The other does not.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/4360464
- author
- Rantzer, Anders
LU
; Rüffer, Björn
and Dirr, Gunther
- organization
- publishing date
- 2013
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- keywords
- stability, Lyapunov functions, monotone systems
- host publication
- IEEE Xplore Digital Library
- publisher
- IEEE - Institute of Electrical and Electronics Engineers Inc.
- conference name
- 52nd IEEE Conference on Decision and Control, 2013
- conference location
- Florence, Italy
- conference dates
- 2013-12-10 - 2013-12-13
- external identifiers
-
- scopus:84902322013
- DOI
- 10.1109/CDC.2013.6760604
- project
- LCCC
- language
- English
- LU publication?
- yes
- id
- 115b002b-100b-40c5-abd8-d8cd71c3ad0e (old id 4360464)
- date added to LUP
- 2016-04-04 09:59:01
- date last changed
- 2024-04-27 12:29:07
@inproceedings{115b002b-100b-40c5-abd8-d8cd71c3ad0e,
abstract = {{Separable Lyapunov functions play vital roles, for example, in stability analysis of large-scale systems. A Lyapunov function is called max-separable if it can be decomposed into a maximum of functions with one-dimensional arguments. Similarly, it is called sum-separable if it is a sum of such functions. In this paper it is shown that for a monotone system on a compact state space, asymptotic stability implies existence of a max-separable Lyapunov function. We also construct two systems on a non-compact state space, for which a max- separable Lyapunov function does not exist. One of them has a sum-separable Lyapunov function. The other does not.}},
author = {{Rantzer, Anders and Rüffer, Björn and Dirr, Gunther}},
booktitle = {{IEEE Xplore Digital Library}},
keywords = {{stability; Lyapunov functions; monotone systems}},
language = {{eng}},
publisher = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
title = {{Separable Lyapunov functions for monotone systems}},
url = {{http://dx.doi.org/10.1109/CDC.2013.6760604}},
doi = {{10.1109/CDC.2013.6760604}},
year = {{2013}},
}